I will spend most of the time formulating Serre's conjecture and explaining some of its applications: for instance, it implies Artin's conjecture for 2-dimensional odd complex representations of the absolute Galois group of Q. I will sketch some of the main ideas in the recent proof of the conjecture in joint work with Wintenberger, as completed by Kisin. I will also explain, if time permits, how our work offers a fresh perspective on Wiles' proof of Fermat's Last Theorem (FLT). For instance it gives a diiferent, in a sense more elementary, aproach to Ribet's level lowering results, a key ingredient in the proof of FLT.